85.27.4 problem 4

Internal problem ID [22596]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. A Exercises at page 60
Problem number : 4
Date solved : Thursday, October 02, 2025 at 08:54:49 PM
CAS classification : [[_high_order, _quadrature]]

\begin{align*} 2 y^{\prime \prime \prime \prime }&={\mathrm e}^{x}-{\mathrm e}^{-x} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0 \\ y^{\prime \prime }\left (0\right )&=0 \\ y^{\prime \prime \prime }\left (0\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.011 (sec). Leaf size: 15

ode:=2*diff(diff(diff(diff(y(x),x),x),x),x) = exp(x)-exp(-x); 
ic:=[y(0) = 0, (D@@2)(y)(0) = 0, (D@@3)(y)(0) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = -\frac {x^{3}}{6}+\sinh \left (x \right )+c_3 x \]

✓ Mathematica. Time used: 0.029 (sec). Leaf size: 27

ode=D[y[x],{x,4}]==Exp[x]-Exp[-x]; 
ic={y[0]==0,Derivative[2][y][0] ==0,Derivative[3][y][0] ==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {x^3}{3}-e^{-x}+e^x+c_2 x \end{align*}

✓ Sympy. Time used: 0.060 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-exp(x) + Derivative(y(x), (x, 4)) + exp(-x),0) 
ics = {y(0): 0, Subs(Derivative(y(x), (x, 2)), x, 0): 0, Subs(Derivative(y(x), (x, 3)), x, 0): 0} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{2} x - \frac {x^{3}}{3} + e^{x} - e^{- x} \]